Exclusion principle and pigeon hole principle are two core principles in combinatorial mathematics, which play an important role in solving counting problems. Their differences are as follows:

1. Inclusion-exclusion principle:

The principle of inclusion and exclusion is used to calculate the number of elements in the intersection and union of multiple sets. In short, it is a counting technique that can be used to solve some overlapping situations. The core idea of the principle of inclusion and exclusion is to calculate the number of elements in each set, then subtract the number of elements in the intersection of two sets, add the number of elements in the intersection of three sets, and so on until the number of elements in the intersection of all sets is added. Exclusion principle is usually used to solve permutation and combination, probability and counting problems.

2. Dove cage principle:

Pigeon hole principle, also known as pigeon nest principle, can be used to solve the distribution problem. In short, it points out that if there are n drawers, m+n- 1 item, then at least one drawer must have two or more items. The core idea of pigeon hole principle is that when the number of items is greater than the number of drawers, at least one drawer must have multiple items. Pigeonhole principle is usually used to solve scheduling, graph theory and pigeon hole problems.

Generally speaking, inclusion exclusion principle and pigeon hole principle are two different concepts and application scenarios in combinatorial mathematics. The inclusion and exclusion principle is used to calculate the intersection of multiple sets and the number of elements in the union set, while the pigeon hole principle is used to solve the allocation problem when there are multiple items in at least one container.